{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9.4. Finding the equilibrium state of a physical system by minimizing its potential energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = 9.81  # gravity of Earth\n",
    "m = .1  # mass, in kg\n",
    "n = 20  # number of masses\n",
    "e = .1  # initial distance between the masses\n",
    "l = e  # relaxed length of the springs\n",
    "k = 10000  # spring stiffness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "P0 = np.zeros((n, 2))\n",
    "P0[:, 0] = np.repeat(e * np.arange(n // 2), 2)\n",
    "P0[:, 1] = np.tile((0, -e), n // 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x7f93deeab668>"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f93deeab668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.eye(n, n, 1) + np.eye(n, n, 2)\n",
    "# We display a graphic representation of\n",
    "# the matrix.\n",
    "f, ax = plt.subplots(1, 1)\n",
    "ax.imshow(A)\n",
    "ax.set_axis_off()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = l * (np.eye(n, n, 1) + np.eye(n, n, 2))\n",
    "for i in range(n // 2 - 1):\n",
    "    L[2 * i + 1, 2 * i + 2] *= np.sqrt(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "I, J = np.nonzero(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dist(P):\n",
    "    return np.sqrt((P[:,0]-P[:,0][:,np.newaxis])**2 +\n",
    "                   (P[:,1]-P[:,1][:,np.newaxis])**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_bar(P):\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(5, 4))\n",
    "\n",
    "    # Wall.\n",
    "    ax.axvline(0, color='k', lw=3)\n",
    "\n",
    "    # Distance matrix.\n",
    "    D = dist(P)\n",
    "\n",
    "    # Get normalized elongation in [-1, 1].\n",
    "    elong = np.array([D[i, j] - L[i, j]\n",
    "                      for i, j in zip(I, J)])\n",
    "    elong_max = np.abs(elong).max()\n",
    "\n",
    "    # The color depends on the spring tension, which\n",
    "    # is proportional to the spring elongation.\n",
    "    colors = np.zeros((len(elong), 4))\n",
    "    colors[:, -1] = 1  # alpha channel is 1\n",
    "\n",
    "    # Use two different sequentials colormaps for\n",
    "    # positive and negative elongations, to show\n",
    "    # compression and extension in different colors.\n",
    "    if elong_max > 1e-10:\n",
    "        # We don't use colors if all elongations are\n",
    "        # zero.\n",
    "        elong /= elong_max\n",
    "        pos, neg = elong > 0, elong < 0\n",
    "        colors[pos] = plt.cm.copper(elong[pos])\n",
    "        colors[neg] = plt.cm.bone(-elong[neg])\n",
    "\n",
    "    # We plot the springs.\n",
    "    for i, j, c in zip(I, J, colors):\n",
    "        ax.plot(P[[i, j], 0],\n",
    "                P[[i, j], 1],\n",
    "                lw=2,\n",
    "                color=c,\n",
    "                )\n",
    "\n",
    "    # We plot the masses.\n",
    "    ax.plot(P[[I, J], 0], P[[I, J], 1], 'ok',)\n",
    "\n",
    "    # We configure the axes.\n",
    "    ax.axis('equal')\n",
    "    ax.set_xlim(P[:, 0].min() - e / 2,\n",
    "                P[:, 0].max() + e / 2)\n",
    "    ax.set_ylim(P[:, 1].min() - e / 2,\n",
    "                P[:, 1].max() + e / 2)\n",
    "    ax.set_axis_off()\n",
    "\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x7157668>"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QlBEfAAAAAACaMuIDAAAAAEBTRnwAAAAAAGjKiA8AAAAA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\n1uzu3bv50Y9+NOnbmGpGfJgi169fn/QtAAAAAMC6/OQnP5n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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7157668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = show_bar(P0)\n",
    "ax.set_title(\"Initial configuration\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def energy(P):\n",
    "    # The argument P is a vector (flattened matrix).\n",
    "    # We convert it to a matrix here.\n",
    "    P = P.reshape((-1, 2))\n",
    "    # We compute the distance matrix.\n",
    "    D = dist(P)\n",
    "    # The potential energy is the sum of the\n",
    "    # gravitational and elastic potential energies.\n",
    "    return (g * m * P[:, 1].sum() +\n",
    "            .5 * (k * A * (D - L)**2).sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.981"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "energy(P0.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "bounds = np.c_[P0[:2, :].ravel(),\n",
    "               P0[:2, :].ravel()].tolist() + \\\n",
    "    [[None, None]] * (2 * (n - 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "P1 = opt.minimize(energy, P0.ravel(),\n",
    "                  method='L-BFGS-B',\n",
    "                  bounds=bounds).x.reshape((-1, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x74b6ef0>"
    }
   },
   "outputs": [
    {
     "data": {
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77LOmLSFiJz4+PoYb6P76669u7E3mwbhiHsYV2B0hPgBkQs7W43vyySctazt/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\nrqSrHrhHQkKCOnfurD///DN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/AAAAAACEMkJ8AOhgmpsdevnlt7V2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\nERERqlevngIDA90+D5cnyPUIAAAAAABA6bR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x74b6ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = show_bar(P1)\n",
    "ax.set_title(\"Equilibrium configuration\")"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 2
}
